SSC MTS 2 Aug 2019 Shift 3 Paper

Let the height of this cuboid be h.
⇒ Total surface area = 2[l × b + b × h + h × l]
⇒ 340 = 2[10 × 8 + 8 × h + h × 10]
⇒ 170 = 80 + 8h + 10h
⇒ 90 = 18h
⇒ h = 5 cm
⇒ The length of the longest stick = diagonal of cuboid
⇒ The length of the longest stick = √ $\left({\mathrm{l}}^2+{\mathrm{b}}^2+{\mathrm{h}}^2\right)$ = √ $\left(100+64+25\right)$ = √189
⇒ The length of the longest stick = 3√21 cm
∴ The length of the longest stick that can be fitted inside the cuboid is 3√21 cm.